Finite Group Databasebeta

← C151×#24509 #50329434

Subgroups — C151×#24509 #50329434

Order 38656.

1034 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#448×C151C211yesmaximal, characteristic
2C2×#432×C151C211yesmaximal, characteristic, complemented
3#2854×C151C211yesmaximal, characteristic
4C2×#391×C151C211yesmaximal, characteristic, complemented
5#2068×C151C212yesmaximal, complemented
6#2055×C151C212yesmaximal, complemented
7#1973×C151C212yesmaximal, complemented
8#1935×C151C212yesmaximal, complemented
9#1874×C151C211yesmaximal, characteristic
10#1852×C151C211yesmaximal, characteristic, complemented
11#1787×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14C2×#123×C151—21no—
15C2×#121×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C42×C151C2211yescharacteristic
18#448×C151—24no—
19#432×C151—24no—
20C2×#107×C151C2212yes—
21C2×C4⋊C8×C151C2212yes—
22C2×#103×C151C2212yes—
23C2×#103×C151C2212yes—
24C2×#103×C151C2212yes—
25C2×#102×C151C2212yes—
26C2×C22⋊C8×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28C2×#97×C151C2212yes—
29#391×C151—21no—
30#391×C151—21no—
31#391×C151C2212yes—
32#391×C151C2212yes—
33#390×C151C2211yescharacteristic
34#390×C151C2211yescharacteristic
35#389×C151C2211yescharacteristic
36#389×C151C2211yescharacteristic
37#388×C151—21no—
38#388×C151—21no—
39#386×C151—21no—
40#380×C151C2211yescharacteristic
41C2×#95×C151—21no—
42C2×#95×C151—21no—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151—21no—
46C22×Q8×C151—24no—
47C22×Q8×C151—22no—
48C22×Q8×C151—22no—
49C22×Q8×C151—42no—
50C22×Q8×C151C2312yes—
51C22×D4×C151—21no—
52C22×D4×C151C2311yescharacteristic
53C23×C4×C151—21no—
54C23×C4×C151—21no—
55C23×C4×C151D411yescharacteristic
56C23×C4×C151D411yescharacteristic
57C23×C4×C151C2311yescharacteristic
58C2×SD16×C151—24no—
59C2×SD16×C151—24no—
60C2×SD16×C151—42no—
61C22×C8×C151C2312yes—
62C22×C8×C151C2312yes—
63#123×C151—44no—
64#121×C151—22no—
65#121×C151—22no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151—42no—
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C4⋊C4×C151C2312yes—
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C22⋊C4×C151—21no—
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151—21no—
78C2×C22⋊C4×C151—21no—
79C2×C22⋊C4×C151—21no—
80C2×C42×C151—22no—
81C2×C42×C151—22no—
82C2×C42×C151D411yescharacteristic
83C2×C42×C151D411yescharacteristic
84C2×C42×C151C2311yescharacteristic
85C2×C42×C151C2311yescharacteristic
86#107×C151—42no—
87C4⋊C8×C151—24no—
88#103×C151—24no—
89#103×C151—24no—
90#103×C151—42no—
91#102×C151—42no—
92C22⋊C8×C151—22no—
93C22⋊C8×C151D414yes—
94#97×C151—24no—
95#95×C151—22no—
96#95×C151—22no—
97#95×C151—22no—
98#95×C151—22no—
99#95×C151—21no—
100#95×C151—21no—
101#95×C151—21no—
102C24×C151—21no—
103C24×C151C2×D411yescharacteristic
104C2×Q8×C151—24no—
105C2×Q8×C151—22no—
106C2×Q8×C151—22no—
107C2×Q8×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151—22no—
110C2×Q8×C151—48no—
111C2×Q8×C151—48no—
112C2×Q8×C151—42no—
113C2×Q8×C151—42no—
114C2×Q8×C151#4114yes—
115C2×D4×C151—21no—
116C2×D4×C151—21no—
117C2×D4×C151—22no—
118C2×D4×C151—22no—
119C2×D4×C151—42no—
120C2×D4×C151—42no—
121C2×D4×C151—42no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—24no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—41no—
136C22×C4×C151—42no—
137C22×C4×C151—42no—
138C22×C4×C151—42no—
139C22×C4×C151—42no—
140C22×C4×C151—42no—
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D412yes—
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151#4112yes—
148C22×C4×C151C2411yescharacteristic
149SD16×C151—48no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C2×C8×C151—22no—
154C2×C8×C151—22no—
155C2×C8×C151C2×D414yes—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—42no—
163C4⋊C4×C151—42no—
164C4⋊C4×C151—42no—
165C22⋊C4×C151—42no—
166C22⋊C4×C151—42no—
167C22⋊C4×C151—42no—
168C22⋊C4×C151—42no—
169C22⋊C4×C151—42no—
170C22⋊C4×C151—42no—
171C42×C151—22no—
172C42×C151—22no—
173C42×C151—21no—
174C42×C151—21no—
175C42×C151—21no—
176C42×C151—21no—
177C23×C151—21no—
178C23×C151—21no—
179C23×C151—21no—
180C23×C151—21no—
181C23×C151—41no—
182C23×C151—41no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151—41no—
187C23×C151—41no—
188C23×C151#12112yes—
189C23×C151AGL(1,ℤ/8)12yes—
190C23×C151#13712yes—
191C23×C151C22×D411yescharacteristic
192Q8×C151—24no—
193Q8×C151—24no—
194Q8×C151—48no—
195Q8×C151—42no—
196Q8×C151—42no—
197D4×C151—42no—
198D4×C151—42no—
199D4×C151—84no—
200C2×C4×C151—21no—
201C2×C4×C151—21no—
202C2×C4×C151—21no—
203C2×C4×C151—21no—
204C2×C4×C151—24no—
205C2×C4×C151—24no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—24no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—44no—
217C2×C4×C151—48no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—44no—
221C2×C4×C151—41no—
222C2×C4×C151—41no—
223C2×C4×C151—42no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—42no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—42no—
233C2×C4×C151—84no—
234C2×C4×C151#12112yes—
235C2×C4×C151#13712yes—
236C2×C4×C151C22×D411yescharacteristic
237C2×C4×C151C2×#4112yes—
238C2×C4×C151C2×#4111yescharacteristic
239C2×C4×C151H(5,𝔽2)12yes—
240C8×C151—24no—
241C8×C151—42no—
242C22×C151—22no—
243C22×C151—22no—
244C22×C151—22no—
245C22×C151—22no—
246C22×C151—22no—
247C22×C151—22no—
248C22×C151—81no—
249C22×C151—81no—
250C22×C151—81no—
251C22×C151—81no—
252C22×C151—81no—
253C22×C151—81no—
254C22×C151—81no—
255C22×C151#46814yes—
256C22×C151C2×#12111yescharacteristic
257C22×C151#52511yescharacteristic
258C22×C151#53511yescharacteristic
259C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C151C2×#13711yescharacteristic
261C22×C151C2×#13711yescharacteristic
262C22×C151#57511yescharacteristic
263C4×C151—22no—
264C4×C151—22no—
265C4×C151—44no—
266C4×C151—41no—
267C4×C151—41no—
268C4×C151—41no—
269C4×C151—81no—
270C4×C151—81no—
271C4×C151—82no—
272C4×C151—81no—
273C4×C151#54612yes—
274C4×C151#55112yes—
275C2×C151—24no—
276C2×C151—161no—
277C2×C151#241111yescharacteristic
278C2×C151C2×#46811yescharacteristic
279C2×C151#305611yescharacteristic
280C2×C151#311211yescharacteristic
281C2×C151#311711yescharacteristic
282C2×C151#321311yescharacteristic
283C2×C151#321811yescharacteristic
284#24509C15111yesmaximal, characteristic, direct product factor, Sylow
285C151#2450911yescharacteristic, direct product factor, Sylow
286C2×#448C2×C15111yescharacteristic
287C2×#432C2×C15111yescharacteristic, complemented
288#2854C2×C15111yescharacteristic
289C2×#391C2×C15111yescharacteristic, complemented
290#2068C2×C15112yescomplemented
291#2055C2×C15112yescomplemented
292#1973C2×C15112yescomplemented
293#1935C2×C15112yescomplemented
294#1874C2×C15111yescharacteristic
295#1852C2×C15111yescharacteristic, complemented
296#1787C2×C15111yescharacteristic, complemented
297C23×Q8C22×C15111yescharacteristic
298C22×SD16C22×C15112yes—
299C2×#123—21no—
300C2×#121C22×C15111yescharacteristic
301C22×C4⋊C4C22×C15111yescharacteristic
302C22×C42C22×C15111yescharacteristic
303#448—24no—
304#432—24no—
305C2×#107C22×C15112yes—
306C2×C4⋊C8C22×C15112yes—
307C2×#103C22×C15112yes—
308C2×#103C22×C15112yes—
309C2×#103C22×C15112yes—
310C2×#102C22×C15112yes—
311C2×C22⋊C8C22×C15111yescharacteristic
312C2×C22⋊C8C22×C15111yescharacteristic
313C2×#97C22×C15112yes—
314#391—21no—
315#391—21no—
316#391C22×C15112yes—
317#391C22×C15112yes—
318#390C22×C15111yescharacteristic
319#390C22×C15111yescharacteristic
320#389C22×C15111yescharacteristic
321#389C22×C15111yescharacteristic
322#388—21no—
323#388—21no—
324#386—21no—
325#380C22×C15111yescharacteristic
326C2×#95—21no—
327C2×#95—21no—
328#340C22×C15112yes—
329#340C22×C15112yes—
330C22×Q8—24no—
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—42no—
335C22×Q8C23×C15112yes—
336C22×D4—21no—
337C22×D4C23×C15111yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C23×C4D4×C15111yescharacteristic
341C23×C4D4×C15111yescharacteristic
342C23×C4C23×C15111yescharacteristic
343C2×SD16—24no—
344C2×SD16—24no—
345C2×SD16—42no—
346C22×C8C23×C15112yes—
347C22×C8C23×C15112yes—
348#123—44no—
349#121—22no—
350#121—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4C23×C15112yes—
356C2×C4⋊C4C23×C15111yescharacteristic
357C2×C4⋊C4C23×C15111yescharacteristic
358C2×C4⋊C4C23×C15111yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42D4×C15111yescharacteristic
368C2×C42D4×C15111yescharacteristic
369C2×C42C23×C15111yescharacteristic
370C2×C42C23×C15111yescharacteristic
371#107—42no—
372C4⋊C8—24no—
373#103—24no—
374#103—24no—
375#103—42no—
376#102—42no—
377C22⋊C8—22no—
378C22⋊C8D4×C15114yes—
379#97—24no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—22no—
384#95—21no—
385#95—21no—
386#95—21no—
387C24—21no—
388C24C2×D4×C15111yescharacteristic
389C2×Q8—24no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—48no—
396C2×Q8—48no—
397C2×Q8—42no—
398C2×Q8—42no—
399C2×Q8#41×C15114yes—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—42no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—41no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4C2×D4×C15111yescharacteristic
427C22×C4C2×D4×C15111yescharacteristic
428C22×C4C2×D4×C15111yescharacteristic
429C22×C4C2×D4×C15111yescharacteristic
430C22×C4C2×D4×C15112yes—
431C22×C4C2×D4×C15111yescharacteristic
432C22×C4#41×C15112yes—
433C22×C4C24×C15111yescharacteristic
434SD16—48no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8C2×D4×C15114yes—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—42no—
449C4⋊C4—42no—
450C22⋊C4—42no—
451C22⋊C4—42no—
452C22⋊C4—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C42—22no—
457C42—22no—
458C42—21no—
459C42—21no—
460C42—21no—
461C42—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23#121×C15112yes—
474C23AGL(1,ℤ/8)×C15112yes—
475C23#137×C15112yes—
476C23C22×D4×C15111yescharacteristic
477Q8—24no—
478Q8—24no—
479Q8—48no—
480Q8—42no—
481Q8—42no—
482D4—42no—
483D4—42no—
484D4—84no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—24no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—44no—
502C2×C4—48no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—84no—
519C2×C4#121×C15112yes—
520C2×C4#137×C15112yes—
521C2×C4C22×D4×C15111yescharacteristic
522C2×C4C2×#41×C15112yes—
523C2×C4C2×#41×C15111yescharacteristic
524C2×C4H(5,𝔽2)×C15112yes—
525C8—24no—
526C8—42no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22#468×C15114yes—
541C22C2×#121×C15111yescharacteristic
542C22#525×C15111yescharacteristic
543C22#535×C15111yescharacteristic
544C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
545C22C2×#137×C15111yescharacteristic
546C22C2×#137×C15111yescharacteristic
547C22#575×C15111yescharacteristic
548C4—22no—
549C4—22no—
550C4—44no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—82no—
556C4—81no—
557C4—81no—
558C4#546×C15112yes—
559C4#551×C15112yes—
560C2—24no—
561C2—161no—
562C2#2411×C15111yescharacteristic
563C2C2×#468×C15111yescharacteristic
564C2#3056×C15111yescharacteristic
565C2#3112×C15111yescharacteristic
566C2#3117×C15111yescharacteristic
567C2#3213×C15111yescharacteristic
568C2#3218×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#432×C151C2semidirect
4. C2×#391×C151C2semidirect
5. #2068×C151C2semidirect
6. #2055×C151C2semidirect
7. #1973×C151C2semidirect
8. #1935×C151C2semidirect
10. #1852×C151C2semidirect
11. #1787×C151C2semidirect
284. #24509C151direct (N × H)
285. C151#24509direct (N × H)
287. C2×#432C2×C151semidirect
289. C2×#391C2×C151semidirect
290. #2068C2×C151semidirect
291. #2055C2×C151semidirect
292. #1973C2×C151semidirect
293. #1935C2×C151semidirect
295. #1852C2×C151semidirect
296. #1787C2×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#448×C1512
C2×#432×C1512
#2854×C1512
C2×#391×C1512
#2068×C1512
#2055×C1512
#1973×C1512
#1935×C1512
#1874×C1512
#1852×C1512
#1787×C1512
#24509151